a line
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An infinite number, since points take up no space.
A line is made up of a large (infinite) number of points. When we say a point is on a line, we mean that it is one of the pints that form the line.
How about 1 and 149. There are an infinite number of pairs, an infinite number of triplets, an infinite number of quadruplets, ... an infinite number of n-tuples. And n, itself, can be infinitely large.
The plane that geometry refers to is not an airplane. A plane is a two-dimensional group of points that goes on infinitely in all directions; made up of infinite line. For example, a rectangle is a plane.
Yes, all geometry planes are infinite and have lines going in every direction, except it doesn't look like that when you see a grid because they only need to include some information for a certain part of a line of the plane. All lines go forever in each direction (left and right), and a grid is made up of lines.